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Reswitchin’ the Night Away!

I see that Enetation lasted about as long as “NetComments”, and have accordingly given up on comments forever. However, before comments bit the dust, I received a missive from someone about the week before last’s article on the old Cambridge Capital Controversy. The thrust of the message went

“But isn’t ‘reswitching’ a completely empirically irrelevant construct, of no relevance to the real world?”

I have two answers to this. Answer number one is that, as a quick inspection below will show, I didn’t mention reswitching even once. An awful lot of the blood, beer and ink spilt during the CCC was indeed spilt over the concept of reswitching, but it’s not central to the argument (or at least, not to the part I presented below, on the logical incoherence of “capital” as an aggregate quantity). You can’t measure the quantity of capital unless you know the rate of profit, so trying to say anything about the “productivity of capital” is always conditional on an assumption about the equilibrium rate of profit, and is for that reason, logically circular. That’s something which doesn’t depend on reswitching.

Reswitching was a consequence of the joint determination of the rate of profit and the measure of the capital stock, which was considered important to the Sraffians. It’s a dramatisation of the concept, because it makes a mockery of the concept of the rate of interest … in the following way:

Let’s consider two different investment projects. I’m going to call one project a “Sandwich Shop”, because it has the standard business school cashflow profile; a big sunk investment up front (negative cashflow), followed by a series of positive cashflows. In fact, it has cashflows thus: Minus 70 in the first year, zero in the second year, 20 in the third, 70 in the fourth, 55 in the fifth and zero thereafter.

The other project is a more speculative venture in which you put down 20 in year one (a negative cashflow) in order to get 102 in year 8, with zero cashflow in between. I’ll call this venture … oh I dunno … “Enetations”.

The business school alumni present will be polishing their calculators at this point. Well, stop that immediately, wash your hands, and consider what happens to the valuations of these two projects as the discount rate changes. In fact, since I don’t expect you to take me at my word, you’ll probably have to do what I did and fire up Excel to see this in action.

At discount rates below 4%, Enetations has a higher value than the sandwich shop. This is fairly intuitive; if the cost of delaying consumption is low, then you don’t mind waiting three years longer for a return.

At a discount rate of 10-15%, the sandwich shop is more valuable than Enetations. Again, no problem here; we could call Enetations a more “roundabout” method of production, or say that it has higher invested capital. If the discount rate were to rise from below 4% to around 10%, we would expect the owners of Enetations-like projects to switch production to sandwich shops. For all I know, that’s what the bastards have actually done.

But what happens at a rate of 25%? Well, by that point, both projects are pretty marginal in net present value terms, but Enetations is actually worth more! If you stick the rate up to 26% it’s even more dramatic; at this discount rate, the sandwich shop has a negative value, while Enetations is still positive!

The very astute indeed will notice that this isn’t actually the reswitching example that was the focus of all the debate in the 70s; what I’ve done is to trick up the phenomenon of multiple internal rates of return into something resembling “reswitching”. But the central economic phenomenon is there, I think, demonstrating that you don’t need to take on board the whole Sraffian framework for the puzzle to exist; you can get into an awful tangle, of the sort where you can’t say anything intelligent about “capital intensity” or “productivity”, without leaving the confines of something as basic and uncontroversial as discounted cashflow analysis.

The link above is to a website dealing with the leasing industry, suggesting that the problem of multiple internal rates of return (and thus potential reswitchings) is a genuine, real-world phenomenon. Lots of people (Stiglitz, as a young man, was in the lead) made many debating points out of the fact that the Cambridge tradition tended to do what I’ve done above — constructing artificial examples out of Excel rather than finding them in actual data. But I think that’s a silly objection. There’s an old proverb which I try to live my life by:

“If something’s not worth doing, it’s not worth doing properly”.

And, as I hope folks have gathered by now, I don’t think that measuring the capital stock is something that’s worth doing at all.

Plans for the rest of this week; a few more silly ideas, to avoid alienating the readership entirely, then wrapping up this theme with my theory that “the equity premium puzzle” is the entire puzzle of capital theory, restated. Then on to the evolutionary psychology crowd ….